To evaluate this double on girl here. We're going to start with the inner integral, and this is with respect to X. So we're gonna go ahead and leave. Why? As a constant so anti driving X squared X cubed over three plus leave the constants one third. And why? And then the anti derivative of X is X squared over two. And then we can fix that. Bring that up in just a minute from 0 to 1 half eso We wanna simplify all of this, which is what's in the brackets first, and then we'll move out to the other in a girl with respect to why? From 1 to 2 and so now substituting here, uh, 0.5 year olds will do this in blue. Well, first off, if we substitute zero, it's going toe. Knock everything out. So we just need to substitute 0.5 in. And so one half. Think of it as a fraction one half cube would be 818 times three. So there'll be 1 24 and then plus Okay, one half here would be, uh, 1/4 times to would be 18 times three. That would also be 1 24. And why? So the wild stays and so now we've and then minus zero. So we've simplified all of that. So then now we're gonna anti derive from 1 to 2 with respect to why So our next step, we just go ahead and keep it. Keep going. Right here is one 24th. Why anti derivative of a constant and then plus one 24th anti derivative of why would be y squared. So let's change that toe. Why? And then the white squared, I should say, divided by two. So this is actually going to become a 40 ft down there. And then all of that is going to be evaluated. Let's switch back to green from 1 to 2. So let's see what this gets us first off to would be, um, to over 24 for just 1 12 plus two squared, um, for over 48 would also be 1 12 and then all of that subtract one 24th and then minus 1 48. So then we could just come up common denominator and the first part so we'll continue up here. So the 1 12 1 12 that would be, um, 2/12 but then multiplied by 48 so that the eight over 48 uh, and then minus to over 22/48 is the same thing. That 1/24 and then minus hope. Sorry. That should be a plus there. But eventually it turns into a minus because of the distributing the minus there and then minus another 1/48. So then we've got, um eight minus 26 minus 15 over 48. So this is our simplified for action here, and we can't simplify it any further.